戴森和库仑博弈
The Dyson and Coulomb games
摘要：
我们介绍和调查某些$N$球员动态游戏的线上和平面上，承认库仑气体动力学作为纳什均衡。最重要的是，我们发现，普遍的局部极限的平衡是敏感的选择模型的球员信息在一维，但不是在二维。我们还发现，玩家可以通过自私的行为实现博弈论的对称性，尽管状态的非交换，这使我们能够建立N-Nash系统对局部最优玩家集合的预期平均场方程的强局部收敛，即，那些表现出与Nash最优集合相同的局部极限的集合。在一维，这种收敛显着特点的非本地到本地的过渡人口依赖的$N$ -纳什系统。
英文摘要：
We introduce and investigate certain $N$ player dynamic games on the line and in the plane that admit Coulomb gas dynamics as a Nash equilibrium. Most significantly, we find that the universal local limit of the equilibrium is sensitive to the chosen model of player information in one dimension but not in two dimensions. We also find that players can achieve game theoretic symmetry through selfish behavior despite non-exchangeability of states, which allows us to establish strong localized convergence of the N-Nash systems to the expected mean field equations against locally optimal player ensembles, i.e., those exhibiting the same local limit as the Nash-optimal ensemble. In one dimension, this convergence notably features a nonlocal-to-local transition in the population dependence of the $N$-Nash system.
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